Scattering Cross Section

散射截面

The concept of cross section, as its name suggests, is that of effective area for collision. The cross section of a spherical target is

截面的概念，如其名称所示，是指碰撞的有效面积。球形靶的截面是

Discussion of cross section

截面的讨论

In aiming a beam of particles at a target which is much smaller than the beam, as in the Rutherford scattering experiment, the cross section takes on a statistical nature.

在将粒子束瞄准一个远小于束流的靶时，例如卢瑟福散射实验中，截面表现出统计性质。

Rutherford worked out the scattering cross section for alpha particles of kinetic energy KE scattering off a single nucleus with atomic number Z. The cross section for scattering at a greater angle than some chosen angle is

卢瑟福推导出了α粒子以动能KE散射 off 一个原子序数为Z的单个核的散射截面。散射角度大于某个选定角度的截面是

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More detail is needed for the prediction of the number of scattering events to expect above that angle. When the details about the beam and target are included, the fractional scattering rate is given by

为了预测超过该角度的散射事件数，需要更多的细节。当包括关于束流和靶的信息时，散射率的分数由

The process for dealing with multiple targets is illustrated below.

For an experiment where projectiles of charge Z = and kinetic energy KE = MeV
are scattered by nuclei of atomic number Z= and mass number A = ,
the scattering cross section is fm² = barns.

If the scattering target is in the form of a thin foil of thickness L = x 10^m
with density = gm/cm³,
the scattered fraction for angles greater than degrees
is expected to be x10^ .

对于一个实验，其中带电粒子的电荷数Z = ，动能KE = MeV，被原子序数Z=、质量数A = 的核散射，散射截面为fm² = 拜耳。如果散射目标为厚度L = x 10^ m的薄箔，密度= gm/cm³，那么大于 degrees角度的散射分数预计为x10^ 。

中文译文中的待填/计算数值依次对应：1：zi 2：ki 3：zt 4：mt 5：cf 6：cb 7：lb 8：lp 9：d 10：ang 11：fb 12：fp。实际数值以上方原输入框为准。

This calculation is designed for the calculation of cross section and scattered fraction only. Note that the standard assumptions of Rutherford scattering apply, so that the calculation works only for film thicknesses of a few micrometers or less. Default values will be entered for unspecified parameters, but all values except the cross section and scattered fraction can be changed.

该计算仅用于计算截面和散射分数。请注意，这里应用的是拉瑟福德散射的标准假设，因此该计算仅适用于几微米或更薄的薄膜。未指定的参数将采用默认值，但除截面和散射分数外，其他所有值均可更改。

Numerical example: gold foil

数值例子：金箔

处理多个目标的过程如下所示

Index

Rutherford concepts

索引：卢瑟福概念

HyperPhysics***** Nuclear

HyperPhysics ***** 核物理

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Scattering Cross Section

散射截面

The concept of cross section, as its name suggests, is that of effective area for collision. The cross section of a spherical target is

截面的概念，如其名称所示，是指碰撞的有效面积。球形靶的截面是

The units of cross section are then area units, but for nuclear scattering the effective area is on the order of the cross sectional area of a nucleus. For a gold nucleus of mass number A=197, the radius determined from the nuclear radius relationship is about 7 fermis.

The most common unit for cross section for nuclear scattering interactions is the barn. The cross section in barns for alpha scattering above a selected angle is a standard part of the analysis of Rutherford scattering. In the case of 6 MeV alpha particles scattered from a gold foil, for example, you don't know the impact parameter for any given alpha particle, so the calculation of the scattered fraction takes on a statistical character. For alpha particles bombarding a gold foil of thicknes 1 micrometer, less than 1 in 100,000 would meet the conditions for scattering at over 140°. The cross section for scattering at smaller angles will be larger, because the alpha doesn't have to come as close to be scattered through the smaller angle. For example, the cross section for scattering through 90° or above is 11.3 barns.

核散射相互作用中最常用的截面单位是巴恩。在选定角度以上的α粒子散射中，以巴恩为单位的截面是瑞利散射分析中的标准部分。例如，在6 MeV的α粒子散射从金箔的情况下，你无法知道任何给定的α粒子的碰撞参数，因此散射分数的计算具有统计性质。对于轰击厚度为1微米的金箔的α粒子，少于1/100000的粒子会满足在超过140°散射的条件。对于较小角度的散射，截面会更大，因为α粒子不需要接近到那么近就能被散射通过较小的角度。例如，散射角度为90°或以上的截面为11.3巴恩。

For neutron scattering, there is no coulomb repulsion, so there is no appreciable scattering unless the impact parameter is less than the effective radius for the strong interaction. Therefore for a given target geometry the cross sections are smaller, typically measured in millibarns.

对于中子散射，没有库仑排斥，因此除非碰撞参数小于强相互作用的有效半径，否则不会发生显著的散射。因此，对于给定的目标几何形状，截面通常较小，通常以毫巴恩（millibarns）为单位进行测量。

Since the probability for interaction depends upon the strength and range of the interaction, the cross-sections for neutrino interactions are very small since they interact only by the weak interaction.

由于相互作用的概率取决于相互作用的强度和作用范围，中微子相互作用的截面非常小，因为它们只能通过弱相互作用发生相互作用。